Guest Post by Willis Eschenbach
One of the most fundamental and far-reaching discoveries in modern thermodynamics is the Constructal Law (see the wiki entry as well). It was first formulated by Adrian Bejan in 1996. In one of his descriptions, the Constructal Law is:
For a finite-size (flow) system to persist in time (to live), its configuration must evolve such that it provides easier access to the imposed currents that flow through it.
Figure 1. An example of the Constructal Law processes at work in a river system. Formation of meanders, followed by cutting through a meander to form an oxbow lake. Image Source.
The Constructal Law has been described as being as important as the first two Laws of Thermodynamics, but most people have never heard of it. What does the Constructal Law mean in plain English, and what does it have to do with the climate?
Here is a different statement (pdf) of the Constructal Law, again from Bejan:
In 1996, the constructal law was formulated and proposed to expand thermodynamics in a fundamental way.
First was the proposal to recognize that there is a universal phenomenon not covered by the first law and the second law. That phenomenon is the generation of configuration, or the generation of ‘design’ in nature.
All thermodynamic systems in nature are flow systems (i.e. live, non-equilibrium systems), and they all have configuration. If they do not have it, then they acquire it, in time. The generation of configuration is ubiquitous, like other phenomena covered by other ‘laws’ in physics. Biological systems are configured. Geophysical systems are configured. Engineering and societal systems are configured. The configuration phenomenon unites the animate with the inanimate. All the other phenomena of physics (i.e. of ‘everything’) have this unifying power. Falling rocks, like falling animals, have weight, conserve energy, generate entropy, etc.
Second was the statement that this universal phenomenon should be covered by the constructal law. This law accounts for a natural tendency in time (from existing flow configurations, to easier flowing configurations). This tendency is distinct from the natural tendency summarized as the second law.
Again not necessarily the clearest statement, but the general idea of the Constructal Law is that flow systems continually evolve, within the physical constraints of the particular system, in order to maximize some variable(s).
A meandering river in bottomland is a good physical example to understand what this means. In the case of a river, what is being maximized by the flow system is the length of the river. However, this ideal condition is never achieved. Instead, the river length oscillates above and below a certain value.
As shown in Fig. 1, in an “S” shaped river, the moving water erodes the outside of the bends and deposits silt on the inside of the bends. Of course, this inevitably makes the river longer and longer. But when the river does this for a while, it gets too stretched out for the land to bear. At some point, the river cuts through and leaves an island and what will become an oxbow lake.
That leaves the river shorter. Again the lengthening process continues, until the river cuts through some other bend and shortens again. And as a result, the length of the river oscillates around some fixed value. It is constantly evolving to maximize the length, an ideal which it never attains.
Now, here’s the point of this whole example. Suppose I didn’t know about this active, evolutionary, homeostatic characteristic of rivers. If someone asked me if a river could be shortened, I’d say “Sure. Just cut through a meander.”. And if I cut through the bend I could physically measure the river length and prove that indeed, the river was shorter.
But would that really make the river shorter?
Of course not. Soon the relentless forces of flow would once again increase the length of the river until the next cutoff forms another oxbow lake, and the cycle repeats.
Net effect of my cut on the length of the river? None. The length of the river continues to oscillate around the same fixed value.
The key to understanding flow systems is that they are always “running as fast as they can”. They are not just idling along. They are not at some random speed. They are constantly evolving to maximize something. The Constructal Law ensures that they are up against the stops, so to speak, always going flat out.
What does all of this have to do with climate? The Earth’s climate is a huge flow system. It circulates air and water from the tropics to the poles and back. As a result the climate, like the river, is subject to the Constructal Law. This means that climate is constantly evolving to maximize something. Climate, like the river, is also “running as fast as it can”.
What does the climate flow system maximize? Because it is a heat engine (converting sunlight into the physical work of the planetary circulation), Bejan says (pdf) that it is doing a dual maximization. It maximizes the sum of the work done driving the planetary circulation, and the heat rejected back to space at the cold end of the heat engine. Again in Bejan’s words:
The earth surface model with natural convection loops allows us to estimate several quantities that characterize the global performance of atmospheric and oceanic circulation. We pursue this from the constructal point of view, which is that the circulation itself represents a flow geometry that is the result of the maximization of global performance subject to global constraints.
The first quantity is the mechanical power that could be generated by a power plant operating between Th and Tl, and driven by the heat input q. The power output (w) is dissipated by friction in fluid flow (a fluid brake system), and added fully to the heat current (qL) that the power plant rejects to Tl.
where Th and Tl are the temperatures of the hot and cold ends of the system. The system is maximizing the sum of work done and heat rejected.
There is a most fascinating interplay between those two. When the speed of the planetary circulation is low, so are the turbulent losses. So as speed increases, up to a certain point the sum of work done (circulation speed) and heat rejected is also increasing.
But as the speed increases further, the turbulence rapidly starts to interfere with the circulation. Soon, a condition exists where further speed increases actually decrease the total of work done and heat rejected. That is the point at which the system will naturally run. This is why nature has been described in the past as running at “the edge of turbulence”.
What does that mean for understanding the climate? This is a new area of scientific investigation. So I don’t know what all of that means, there’s lots of ramifications, some of which I may discuss in a future post. However, one thing I am sure of.
If we want to understand the climate, or to model the climate, we have to explicitly take the Constructal Law into account.
We are not modeling a simple system with some linear function relating forcing and response. That kind of simplistic understanding and modeling is not valid in the type of system where, for example, cutting a river shorter doesn’t make it any shorter. We are modeling a dynamic, evolving system which may not be affected by a given forcing. The modelers claim (falsely, but we’ll let that be) that their models are based on “physical principles”.
However, they have left one central, vital, physical principle out of the mix, the Construcal Law. And at the end of the day that means that all of their modelling is for naught. Sure, they can tweak the model so that the output resembles the actual climate. But the actual system does not change over time in a random way. It is not driven here and there by forcing fluctuations. It changes in accordance with the Constructal Law. The future evolution of the climate, what Bejan calls the “generation of configuration”, is ruled by the Constructal Law. It cannot be understood without it.
PS – For those that think that the Constructal Law is some crackpot theory, it is not. Bejan is one of the 100 most cited engineering authors of our time, and the results of the Constructal Law have been verified in a host of disciplines. It is indeed a new fundamental law of thermodynamics, one which we cannot ignore.
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Greg Cavanagh says:
November 15, 2010 at 8:10 pm
This is exactly why the Constructal Law is a fundamental law with applications in so many fields of science. It applies to all flow systems, not just one or two, and it makes no difference what is flowing.
Pamela Gray says: at 6:58 pm …over the top windy
For those not familiar with Pamela’s part of the world here is a rough translation of her technical jargon – complements of the Pendleton NWS:
WINDS: WEST TO NORTHWEST WINDS BETWEEN 35 TO 45 MPH WITH
GUSTS TO AROUND 60 MPH ARE EXPECTED. LOCAL GUSTS TO 70 MPH
ARE POSSIBLE.
willis writes:
“Bejan didn’t get to be one of the top cited scientific authors on the planet by writing foolishness, by being “all bun, no meat”, or by “handwaving”. C’mon, do your homework before uncapping your electronic pens …”
I bet Michael Mann has been cited far more times than Bejan.
Food for thought.
Willis,
Thanks for the post.
I do not see how this expands on general/basic thermodynamics concepts.
In what fundamental way does it add to the basic / general applied science of thermodynamics?
Is it a useful engineering application tool instead of a basic new law? Tool is my impression based on your post.
John
This reminds me of the big red spot predicted by climate models.
http://sciencespeak.com/MissingSignature.pdf
If the air temp is increased by co2 at the equator, then a reaction must take place to accommodate this. Could this reaction be based on the Construction law?
Could the increase in lower level temperature actually increase the convection rate to space?
http://en.wikipedia.org/wiki/File:Convection-snapshot.gif
And eventually cause a slight increase in radiation to space? With an overall balancing effect?
Willis:
This (or something akin to it) may indeed be what is missing from climate and other finite difference models. I’ve never been comfortable with the idea that climate, with all its apparent symmetry, could be chaotic. I’ve thought that this was a cop out for poor modeling.
Such models resolve linearly when we know from empirical evidence that the processes they model (mimic) are cyclical. The push-pull between order and disorder that can be observed in natural systems is nicely accounted for with the Constructal Law.
Now all that is needed is for some math wizards to wrap it all up in a series of formulas that can used to model climate, fluvial flow, crustal motion, planetary and galactic motion, etc. All well beyond my age and talents, but there is bound to be some 20 year old (i.e. fresh) brains out there somewhere ready to work this for the next 20 years.
Well, there is a portion of this that is left out. One of the reasons the Mississippi has lost length is because of levees. What normally happens is that a river drops silt along its travel. At some point the river and its surrounding flood plain is a little higher in altitude than some surrounding ground from all the deposited silt. Then one day there is a flood and the river finds a lower level outside of its regular bank and begins to cut a new channel and a meander is born. If the Mississippi were left on its own, its total length wouldn’t change much. As old meanders are cut off in oxbow lakes, new meanders are formed someplace else.
Levees prevent the river from spreading out. As are result, the channel silts up and you must either continue making the levees taller or you must dredge the channel. In many portions of the Southern Mississippi, you have to look UP to see ships passing on the channel if you are standing away from the levee. The channel is tens of feet higher now than when those levees were first formed.
At some point those levees will fail and the river will cut a new channel. We have been fighting the river trying to cut a new channel for decades down the Atchafalaya. (See Old River Control Structure: http://www.johnweeks.com/river_mississippi/pages/lmiss23.html )
Some day the river will win.
Interesting. The first thought I had “Is this truly a fundamental law or just a result of the interaction of more fundamental laws such as gravity, 1st & 2nd law etc?”
Care to comment?
Has this been proven?
If it is a result of interaction of other laws & those laws are incorporated in the climate models, might they then actually have the constructal law built into them, even if unintentionally?
Okay, so Michael Mann isn’t a highly cited researcher.
But Phil Jones is.
http://hcr3.isiknowledge.com/author.cgi?&link1=Search&link2=Search%20Results&AuthLastName=jones&AuthFirstName=philip&AuthMiddleName=&AuthMailnstName=&CountryID=-1&DisciplineID=0&id=1306
“I’ve never been comfortable with the idea that climate, with all its apparent symmetry, could be chaotic”
That’s because it is not – if it were the whole concept of ‘climate’ would not exist – you would just have weather.
Rivers, rivers of energy, the flow of the cosmos, Victor Schauberger had it nailed.
Come to think of it, even entropy is purely subjective, it depends upon the perspective.
The total availability of energy in a system is a direct function of the data density thus entropy is purely a manifestation of data flow.
John Hultquist and Pamela Gray- winds starting the Grande Ronde Valley, seemed to have calmed a bit, waiting for the front to get here.
Fond memories of flying scheduled air freight/courier this time of year, this is getting to
the point where the only reason to check weather is to see how scared yo are going to get…
As for the name of Grande Ronde, the name was from a French Fir Trapper, name of
Dawes, who described those meanders in the valley. Much like what Willis is talking about…[googlemaps http://maps.google.com/maps?q=Grande+Ronde+Valley&oe=utf-8&client=firefox-a&ie=UTF8&hl=en&hq=&hnear=Grande+Ronde+Valley,+La+Grande,+Union,+Oregon+97850&ll=45.402789,-117.905617&spn=0.058817,0.103512&t=h&z=13&output=embed&w=425&h=350%5D
Smokey says:
November 15, 2010 at 8:49 pm
Thanks, Smokey. One of the advantages to analyzing the climate as a heat engine is that it allows us to to make sense of some of the differences between the tropics and the poles.
A heat engine is characterized in part by two temperatures, Th and Tl. Th is the high temperature of the hotter end of the heat engine. This is the area where the majority of the energy enters the system. Tl is the lower temperature of the colder end(s) of the heat engine. This is the area where excess heat is radiated from the heat engine. In the climate system, the hot end of the heat engine is the tropics and the cold end is the poles.
The Constructal Law says that there will be a constant change and evolution in Th and Tl, accompanied by changes in w, the power expended to circulate the fluid (which is also entropy, since it is all eventually converted to heat by a fluid brake), and Ql, the heat rejected from the tropics to the poles. These quantities will adapt and evolve constantly in such a way as to maximize the sum of w and Ql.
In the tropics, there is a strong governing system which keeps the tropical temperature within fairly narrow bounds. As a result, when there is excess solar energy entering the tropics, the tropics doesn’t heat up much. Instead, the rate at which energy is passing through the heat engine increases. In other words, more heat is exported to the poles rather than being used to warm the tropics.
This, of course, tends to warm the poles. However, because of the homeostatic nature of the Constructal Law, the net result of the changes in Tl and Th are such that the sum of w work done and Ql heat rejected tends to a maximum. As a result, there is no simple one-to-one relationship between forcing changes and changes in either Tl or Th.
Finally, please note that in addition to the climate as a whole, all flow sub-systems of the climate are governed by the Constructal Law. These include such things as the jet streams; the flow of energy into and out of the ocean, land and atmosphere; the oceanic currents; storms and hurricanes; and all types of winds. The complexity of the interplay of these flow systems, each of which is constantly evolving and reorganizing to maximize flow, and many of which form physical constraints for neighboring flow systems similarly evolving, is staggering.
However, please do not mistake this for an “argument from complexity”. I am not saying we cannot understand the climate simply because of its complexity. Quite the opposite.
I am trying to unravel the exact style and nature of the complexity, in order to better understand and model it. Our current generation of models don’t do any better at estimating the uncertainty in climate sensitivity than did the models of twenty years ago. I say it is because they are using the wrong paradigm, one which doesn’t contain the Constructal Law.
Willis, everybody who has had a course in theoretical mechanics will recognize:
Action minimization. From Wikipedia:
In physics, action is an attribute of the dynamics of a physical system. It is a mathematical functional which takes the trajectory, also called path or history, of the system as its argument and has a real number as its result. Action has the dimension of energy × time, and its unit is joule-seconds in the International System of Units (SI). Generally, the action takes different values for different paths. Classical mechanics postulates that the path actually followed by a physical system is that for which the action is minimized, or, more strictly, is stationary. The classical equations of motion of a system can be derived from this principle of least action. The stationary action formulation of classical mechanics extends to quantum mechanics in the Feynman path integral formulation, where a physical system follows simultaneously all possible paths with amplitudes determined by the action. It also provides a basis for the development of string theory.
I make a guess it is a thermodynamic manifestation of the action principle, though I would have to read up to make any better comparison, and even then. Have you not seen any such correlation in your readings?
Willis: The reason nobody’s heard of the ‘constructional law’ is because it isn’t useful. It isn’t useful because everything that might be concluded from it can be concluded from other sources. Where are the great accomplishments, the mind-blowing apocalypses from this law? It sounds like the latest socially-acceptable fraud to me. I give it 10 years before everyone figures out it’s like Michel Foucault all over again. I think you’ve been played. Why is this ‘law’ only showing up in relation to climate sites and the paranormal?: http://reporter.blackraiser.com/?p=909
Furthermore, you should know better than this: “PS – For those that think that the Constructal Law is some crackpot theory, it is not. Bejan is one of the 100 most cited engineering authors of our time, and the results of the Constructal Law have been verified in a host of disciplines. It is indeed a new fundamental law of thermodynamics, one which we cannot ignore. ” Have you lost your mind? The “top” 100 cited climate scientists are all warmists, right?
Thank you Willis!!!
The accreting river is the source of oxbows. Some rivers cut and some accrete and most do both at various points, depending on the available gradient.
The accreting river needs to find a place to drop the sediment load, and that is on the bottom unless in periods of high flow. I seem to recall that a stream’s ability to carry debris increases as the square of the increase in velocity.
Rivers may or may not support or refute Willis’ formulation of law, but they quite clearly react to the external forces of available drop in elevation and composition of the terrain.
John McPhee has written about this in The Control of Nature.
I suspect the heat engine just pumps heat a little further poleward when it’s got more energy to reradiate to space and not so toward the poles when it’s got less. The heat is more easily lost poleward. CO2 concentration somewhat irrelevant. A self-leveling mechanism without the need for a thermostat.
=============
anna v says:
November 15, 2010 at 10:09 pm
Interesting, anna. I had only a vague idea of the action principle, so I read your citation and a couple others. Can’t say I’ve moved too far forwards … there are obvious similarities, although one is a minimization function and the other a maximization function.
Further deponent saith not …
Willis Eschenbach says:
November 15, 2010 at 10:56 pm
For a finite-size (flow) system to persist in time (to live), its configuration must evolve such that it provides easier access to the imposed currents that flow through it.
Sounds to me that “easier access to the imposed currents” means less energy expenditure. That is where minimization would come in.I cannot guess how to write an action integral for flow though. It needs a theoretician.
Thank you Willis, for once again provoking our thoughts.
This phenomenon has been demonstrated and worked out in the statistics of bottlenecks in traffic patterns, applied at once to the traffic “humping along” or “caterpillar crawling” as a response to congestion and density of the traffic. The statistics were worked out for key variables including traffic density, i.e. numbers of cars on a road, width of the lanes, and maximum average speed, and others. Although the traffic, even with a total bumper-to-bumper density, would be physically able to go at the speed limit, say 65 miles per hour, the cars go in fits and starts around an average speed that is allowable under the constraints of the variables, but at a rate much lower than the maximum, and this new value is based on statistical principles.
This has also been applied to military congestion on a battlefield, and I have seen the papers on this years ago. The gist of it is that certain bottlenecks control the flow on a battlefield in a way that is counterintuitive, because the apparent bottlenecks or restrictions one could see as restricting flow are not the ones the statistics finds in practice, but the restrictions happen well ahead or behind or to side eddies of the eye-identified bottlenecks.
Has anyone remembered the work that I am trying to recall?
The new law is also applicable to politicians expounding new policy initiatives. Their explanations become ever more convoluted as confounding issues are identified, until someone cuts through the “spin” with a simple policy explanation. Then, as other politicians add their “two bobs worth” (“five cents worth”), the “spin” process recommences.
http://www.sciencedirect.com/science?_ob=ArticleURL&_aset=V-WA-A-W-A-MsSWYWW-UUA-U-AAVUZBZYVY-AABYWADZVY-ZUDBDCYCD-A-U&_rdoc=1&_fmt=summary&_udi=B6V3H-4J2W0N2-4&_coverDate=01%2F19%2F2006&_cdi=5731&_orig=search&_st=13&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=89441fb0b28e21ddd42397b12bbd20de
Seems like observations are consistent with the law ( I’d like to see the math) they say that since the observations are consistent with the theory that this counts in favor of the theory. Same argument holds true for GCMs.
JDN says: (November 15, 2010 at 10:25 pm) Willis: The reason nobody’s heard of the ‘constructional law’ is because it isn’t useful.
JDN: There is something very appealing to me in your line. It rings true; and I suspect it is.
Steve Mosher, thanks for the link. That appears to be an update and extension of the paper that I linked to above. I’m in the Solomon Islands at the moment, where the electrons move slowly, so I’ll wait until I get back to the US on Friday to download it … $35.95 … grrr.